Two goals from Bundesliga top scorer Robert Lewandowski allowed champions Bayern Munich to forget about their mounting injury woes as they cruised past Augsburg 3-1 to stay eight points clear at the top.

The win not only helped them to move closer to a fourth successive league title but also showed the depth of their talent as Bayern rebounded from losing their fourth central defender to injury.

Following injuries to Javi Martinez, Medhi Benatia and Jerome Boateng, Holger Badstuber joined the casualty list on Saturday after he broke his ankle in training.

"What happened to Holger is a nightmare," Bayern coach Pep Guardiola told reporters.

Badstuber, who has suffered a string of injuries since 2012, is expected to be sidelined for three months.

On the field, Bayern quickly took control and Lewandowski impressively shook off three defenders to turn and drill in for the lead in the 15th minute.

The Poland forward, who had also scored twice in their midweek 3-0 German Cup win over VfL Bochum, took his league tally to 21 goals after he latched on to a perfectly-timed Thiago Alcantara pass to float the ball past keeper Marwin Hitz in the 62nd minute.

Since the resumption of the Bundesliga following the winter break, Lewandowski had been the only Bayern player to score in the league -- finding the net six times in four games -- but all that changed in the 78th minute when Thomas Mueller slotted in his 15th goal of the season.

Raul Bobadilla grabbed a late goal for the hosts as Bayern moved to 56 points thanks to their 18th win in 21 Bundesliga matches.

Guardiola, however, warned mounting injuries could be a problem when they take on Juventus in the Champions League round of 16 later this month.

"This is no ideal situation. We are up against one of the best teams in Europe," said the Spaniard, whose team is chasing a treble of titles.

Borussia Dortmund are second on 48 following their 1-0 victory over Hanover 96 on Saturday with Bayer Leverkusen in third on 35.